Convex expectations for countable-state uncertain processes with càdlàg sample paths

IF 3.2 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE International Journal of Approximate Reasoning Pub Date : 2024-10-18 DOI:10.1016/j.ijar.2024.109308
Alexander Erreygers
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Abstract

This work investigates convex expectations, mainly in the setting of uncertain processes with countable state space. In the general setting it shows how, under the assumption of downward continuity, a convex expectation on a linear lattice of bounded functions can be extended to a convex expectation on the measurable extended real functions. This result is especially relevant in the setting of uncertain processes: there, an easy way to obtain a convex expectation on the linear lattice of finitary bounded functions is to combine an initial convex expectation with a convex transition semigroup. Crucially, this work presents a sufficient condition on this semigroup which guarantees that the induced convex expectation is downward continuous, so that it can be extended to the set of measurable extended real functions. To conclude, this work looks at existing results on convex transition semigroups from the point of view of the aforementioned sufficient condition, in particular to construct a sublinear Poisson process.
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具有 càdlàg 样本路径的可数状态不确定过程的凸期望值
这项工作主要是在具有可数状态空间的不确定过程的背景下研究凸期望。在一般情况下,它说明了在向下连续性假设下,有界函数线性网格上的凸期望如何扩展为可测扩展实函数上的凸期望。这一结果与不确定过程的设置尤其相关:在不确定过程中,获得有限有界函数线性网格上的凸期望的简单方法是将初始凸期望与凸过渡半群结合起来。最重要的是,这项研究提出了一个关于这个半群的充分条件,它保证了诱导凸期望是向下连续的,因此它可以扩展到可测量的扩展实函数集合。最后,本作品从上述充分条件的角度出发,研究了凸过渡半群的现有结果,特别是构建了一个亚线性泊松过程。
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来源期刊
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning 工程技术-计算机:人工智能
CiteScore
6.90
自引率
12.80%
发文量
170
审稿时长
67 days
期刊介绍: The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
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